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Chapter 15: Q3MP (page 776)

There are 3 red and 2 white balls in one box and 4 red and 5 white in the second box. You select a box at random and from it pick a ball at random. If the ball is red, what is the probability that it came from the second box?

Short Answer

Expert verified

The Probability is found to be p(S/R)=2047and it can be shown with the picture given below.

Step by step solution

01

Given Information. 

It has been given that there are 3 red and 2 white balls in one box and 4 red and 5 white in the second box.

02

 Step 2: Definition of Probability.

Probability means the chances of any event to occur is called it probability.

03

Find the probability.

Find the Probability of the red ball.

p(R)=p1R+p2R=0.5×35+0.5×49=4790n

If the ball is red the probability that it comes from the second box is derived below.

p(S/R)=p(SR)p(R)=0.5×4947/90=2047

04

Draw the diagram to show the situation. 

The situation is shown below.

The Probability is shown below.

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Most popular questions from this chapter

Three coins are tossed; x = number of heads minus number of tails.

A weighted coin with probability p of coming down heads is tossed three times; x = number of heads minus number of tails.

(a) Following the methods of Examples 3,4,5, show that the number of equally likely ways of putting N particles in n boxes,n>N, nNisfor Maxwell Boltzmann particles, C(n,N)for Fermi-Dirac particles, C(n−1+N,N)andfor Bose-Einstein particles.

(b) Show that if n is much larger than N (think, for example, ofn=106,N=10), then both the Bose-Einstein and the Fermi-Dirac results in part (a) contain products of N numbers, each number approximately equal to n. Thus show that for n N, both the BE and the FD results are approximately equal tonNN!which is1N!times the MB result.

(a) Set up a sample space for the 5 black and 10 white balls in a box discussed above assuming the first ball is not replaced. Suggestions: Number the balls, say 1 to 5 for black and 6 to 15 for white. Then the sample points form an array something like (2.4), but the point 3,3 for example is not allowed. (Why?

What other points are not allowed?) You might find it helpful to write the

numbers for black balls and the numbers for white balls in different colors.

(b) Let A be the event “first ball is white” and B be the event “second ball is

black.” Circle the region of your sample space containing points favorable to

A and mark this region A. Similarly, circle and mark region B. Count the

number of sample points in A and in B; these are and . The region

AB is the region inside both A and B; the number of points in this region is

. Use the numbers you have found to verify (3.2) and (3.1). Also find

and and verify (3.3) numerically.

(c) Use Figure 3.1 and the ideas of part (b) to prove (3.3) in general.

Set up several non-uniform sample spaces for the problem of three tosses of a coin
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